Internic whois lookup: this looks up the registered operator of a given domain name, along with their DNS servers (which may be operated by their hosting provider, but which could also easily be hosted elsewhere).

That will get you started. For more detailed information, use the traceroute command (or "tracert" on Windows) to see the path between your point on the network, and theirs.

The nameserver data from whois seems to be a better indicator of the hosting provider than the domain owner/operator.
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HafthorMay 14 '09 at 21:53

Absolutely, but again, you should definitely take it with a large grain of salt: just because the website is hosted with a particular provider, doesn't mean the DNS is hosted by them as well. I'd typically defer to the ARIN lookup data if you're primarily interested in the (web/application) hosting provider, as well as the traceroute information.
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esmMay 14 '09 at 22:10

This will also depend on whether the domain is owned and registered by the hosting provider or not. The best clue normally is the DNS records, however I used to roll my own DNS for a while using zone edit for example, and non of the domain queries would show who is hosting the domain.

However it should give you fairly accurate information as to who owns the domain.